Multi-stage supply network design in case of reverse flows: a closed-loop approach

Int. J. Operational Research, Vol. 12, No. 2, 2011 157

Copyright © 2011 Inderscience Enterprises Ltd.

Multi-stage supply network design in case of reverse flows: a closed-loop approach

Maurizio Faccio*, Alessandro Persona, Fabio Sgarbossa and Giorgia Zanin Department of Innovation in Mechanics and Management, University of Padua, Via Venezia 1, Padua 35131, Italy Fax: +39 49827681 E-mail: [email protected] E-mail: [email protected] E-mail: [email protected] E-mail: [email protected] *Corresponding author

Abstract: Design of distribution networks is one of the most critical issues in the management of supply networks. When the supply chain takes into account the whole life of the product (warranty, remanufacturing, recycle, disposal, etc.), the adverse effects on the logistic flow is quite considerable on the structure of the network. For this reason, these aspects should be considered in network design. This paper addresses the possibility to apply different supply chain (SC) design approaches in presence of reverse flows, analysing the network structure where the considered flows are forward flow exclusively, or forward and reverse flows, or integral closed-loop flows. The study also presents an integrated methodology in closed-loop network design, based on mixed-integer programming, considering as inputs the most important driver as fixed and variable costs (installation, transportation, handling, inventory and production), facilities attributes (type, location, capacity and costs), stochastic demand, multi-echelon, multi-product, multi-production, multi-distribution and multi-transportation system. A real industrial application to validate the proposed closed-loop SC design methodology and a comparison between different SC design approaches are presented as a result of this paper.

Keywords: distribution network; distribution costs; transport; linear programming; supply chain management; reverse logistics; closed-loop network.

Reference to this paper should be made as follows: Faccio, M., Persona, A., Sgarbossa, F. and Zanin, G. (2011) ‘Multi-stage supply network design in case of reverse flows: a closed-loop approach’, Int. J. Operational Research,Vol. 12, No. 2, pp.157–191.

Biographical notes: Maurizio Faccio is an Assistant Professor in Industrial Plants and Logistics. In December 2003, he graduated in Engineering Management at the University of Padua with evaluation 110/110 cum laude, discussing a thesis concerning ‘Mixed-model assembling line balancing problem’. Since June 2006, he has been an Assistant Professor in the Faculty of Engineering at the University of Padua in ING-IND/17 SDS. Since January 2004, he has been carrying out his own research activities at the University of

158 M. Faccio et al.

Padua inside research team coordinated by Professor Alessandro Persona. This team (SSD ING-IND/17) has been evaluated as ‘very good-excellent’ research group by an international panel of referee that analysed five years of activities of DTG department. This small group has excellent scientific production and funding from local industry. Overall assessment: very good – excellent. He is the author and co-author of more than 40 papers in international journals and conferences. The principal activities of his research are focused on industrial systems and services, industrial system design, productive plant design, production and logistic system management.

Alessandro Persona is a Full Professor in Industrial Plants and Logistics. This team (SSD ING-IND/17) has been evaluated as ‘very good-excellent’ research group by an international panel of referee that analysed five years of activities of DTG department. This small group has excellent scientific production and funding from local industry. Overall assessment: very good – excellent. Recently, he received the Best Paper Award (2008) for the paper ‘A single-vendor multi-buyer consignment stock inventory model’ written with Battini, Faccio and Sgarbossa, during GBID (BIRC, Emerald, Elsevier, Science Direct Conference) in Rio De Janeiro. Currently, he is an Editorial Board Member of the Int. J. Operational Research, and he is going to enter into the Editorial Board of the Int. J. Procurement Management. He belongs to the Committee of ISSAT (USA), GBID (USA) and acts as referee for important international journals. He is the author and co-author of more than 100 papers in international journals and conferences.

Fabio Sgarbossa is an Assistant Professor at University of Padua. Since 2010, he is a PhD in Mechatronics and Industrial System at the University of Padova. He is carrying out his own researches in the Department of Innovation in Mechanics and Management. Since 2005, he has been carrying out his research inside the team coordinated by Professor Alessandro Persona. In 2008, he was Visiting Researcher in the Department of Industrial and Systems Engineering at Rutgers University. Also he is a Member of the IEEE and IIE. The main activities of his research concern advanced methodologies in production and logistics, from the material handling to maintenance, from productive system management to distribution systems through frequent private collaborations. He is the author and co-author of more than 40 international scientific publications about Industrial Plants Design and Management, Maintenance, Industrial Logistics.

Giorgia Zanin is a PhD Student in Mechatronics and Industrial System at the University of Padua. She has been carrying out her own research in the Department of Management and Technology at the University of Padua. Her main work focuses on advanced technologies in logistic traceability and on supply chain network design and management.

1 Introduction

In the last decades, the design and management of supply networks have been fully studied in the scientific literature. It encompasses all goods, movements and storage, including raw materials, work-in-process inventory and finished goods from the point-of-origin to the point-of-consumption (Melo et al., 2009).

Multi-stage supply network design in case of reverse flows 159

From the point of view of material flows, it is possible to classify three basic network structures (Kannan et al., 2010):

Forward supply chain (FSC): a FSC is a network of facilities and distribution options that performs the functions of materials procurement, transformation into intermediate and finished products and distribution to customers.

Reverse supply chain (RSC): RSC focuses on the backward flow of materials from customer to supplier (or alternate disposition) with the goal of maximising the value of the returned item or minimising the total reverse logistics cost.

Closed-loop supply chain (CLSC): A CLSC consists of both the FSC and the RSC. The FSC involves mainly the movement of goods/products from the upstream suppliers to the downstream customers, whereas the RSC involves the movement of used/unsold products from the customer to the upstream supply chain, for possible recycling and reuse. It is possible to distinguish between two different CLSC designs: the sequential CLSC, in which the reverse flow is independent of the forward flow, and the integral CLSC, in which the route in the reverse flow is the same as the one in forward flow, including the same transportation model to optimise transportation costs (Fleischmann et al., 2001).

While for the traditional FSC, several years of application have produced an extensive array of models to support network design tasks, whereas for RSC, the attention is more recent and the availability is not as vast. In addition, the models are divided into three groups to support three different realities that demand a RSC (Wang et al., 2007): economic aspects (the possibility of recapturing value from used products), government directives (European Union WEEE Directive, 2007) and consumer pressure (e.g. return of defective products).

In a world of increasing environmental concerns, strict regulations on waste and the trend towards environmentally friendly products from inception of the production phase, through the life and disposal of the product itself (Kannan et al., 2010), the necessity to obtain management models to assist in the creation of CLSCs is becoming more pressing.

Fleischmann et al. (2001) asked about RSC: “How robust are traditional logistics networks when it comes to addressing product recovery activities?” To make a generalisation, their conclusion was the following: forward flows dominate the network design. The impact of return flows increases with the economic incentive for product recovery (namely higher production savings, higher penalty costs for refusing to collect end of life products and higher disposal costs) and with a decrease in the number and uniformity of potential facility locations. Taking the study one step further, we only found a significant impact of return flows on the forward network (and hence a cost difference between the integral and sequential design) in case of a major structural difference between forward and reverse channel cost structures, when added to high return volumes. If product recovery can, in many cases, be implemented without major changes in existing forward production–distribution networks, it is also true that separate


networks can be expected to be much easier to deal with organisationally. A company can create a new, dedicated organisational unit to deal with return flows, which would lower coordination and restructuring costs. From a methodological point of view, they observed that forward and return networks can be modelled separately in many cases, which significantly reduces the problem sizes.

Today, for the importance of both direct and reverse logistic flows, in terms of volumes and reverse flows activities (i.e. inspection stage, separation stage, etc.) it often requires an integrated approach of supply chain (SC) models. Forward and return networks cannot be modelled separately for various reasons: firstly, the minimisation of the global logistics cost is not always given by the individual minimisation of direct logistic costs and reverse logistic costs separately, and secondly, the combined effect of direct and reverse flows is further amplified when considering installation, transportation, handling, inventory and disposal activities.

The main contributions of this paper are:

To understand when it is actually effective to model direct and reverse flows separately, in function of their quantity and the facility constrains, reducing the problem size, applying FSC or RSC model instead of the more complex CLSC models.

To overtake the focalisation on just some dimensions of the CLSC design problem of many studies presented in scientific literature (i.e. SC design with limited number of products, limited transportation modes, no capacity constrains, no inventory or other kind of costs considered, etc.), developing a CLSC design model that aims to consider, with an integrated approach, the key aspects in strategic configuration of supply networks.

Section 2 presents a brief review of the existing literature on SCM, and Section 3 focuses on the cost drivers of each type of supply chain. A new integrated methodology, based on mixed-integer programming, is described in Section 4 and Section 5, where practical applications and results are discussed in detail. Conclusions are reported in Section 6.

2 Literature review

Decisions about the right type of distribution system to implement are a strategic issue for almost every company. The problem of locating facilities and allocating customer covers the core components of distribution system design (Klose and Drexl, 2005). The so-called location–allocation problem is not new to the operations research community and has been the subject of several papers and books.

The present literature review analysed the study about the SCM from the point of view of material flows:

forward supply chain

reverse supply chain

closed-loop supply chain.

The decision models on forward supply chain (FSC) design have been recently collected in two surveys developed by Meixell and Gargeya (2005) and Van der Vaart and


van Donk (2008) was analysed many literature review such as Meixell and Gargeya (2005) and Van der Vaart and van Donk (2008) that studied decision support models for the design of global supply chains. The first one considered the fit between the research literature in this area and the practical issues of global supply chain design, whereas the second highlighted the relationship between supply chain integration and performance. ReVelle and Eiselt (2005) distinguished between location problems and layout problems, whereas ReVelle et al. (2008) considered the median and plant location models, and centre and covering models. Klose and Drexl (2005) suggested a classification that distinguishes continuous location models, network location models, mixed-integer programming models and applications. This classification was repeated in Melo et al. (2009), where the authors discussed the general relation between facility location models and strategic supply chain planning.

As previously emphasised, we can find many different models applicable to SCM, such as the continuous location model, which includes the Weber problem analysed in many papers. Canbolat and Wesolowsky (2010) considered the problem of locating a single facility in the presence of a line barrier that occurs randomly on a given horizontal route, and Bischoff and Klamroth (2007) and Bischoff et al. (2009) considered the problem of locating new facility with respect to a given set of existing facilities and the presence of convex polyhedral barriers. Another model available in literature is the mixed-integer model, like the one proposed in Amiri (2006) for the location of the production plants and distribution warehouses and definition of the best distribution strategy, while Wu et al. (2006) presented an extension of the capacitated facility location problem, in which the general set-up cost functions and multiple facilities in one site were considered. Instead, Harkness and ReVelle (2003) proposed a new type of hybrid facility location model derived from the well-studied simple uncapacitated and capacitated facility location models, and Alumur and Kara (2008) classified and surveyed the network hub location model.

Many papers did not consider the location problem exclusively but analysed the interaction with other features. Erlebacher and Meller (2000) and Miranda and Garrido (2007) considered the interaction between location and inventory in designing distribution systems. Max Shen and Qi (2007) and Ambrosino and Scutella (2005) analysed some integrated models relative to location, allocation, inventory and routing decision. Lin et al. (2009) considered the vehicle routing aspect and proposed a simulated annealing-based heuristic for solving the location routing problem. Also, Nozick and Turnquist (2001) considered an integrated approach, and in addition to the location routing problem, they also considered the service responsiveness. Battini et al. (2007) considered the optimisation of goods delivery policies in a distribution network and contributed to the development of a procedure, taking into consideration both batch production environment and limited capacity of manufacturer plant warehouses. Balaji and Jawahar (2010) analysed a two-stage distribution problem of a supply chain associated with a fixed charge.

All the papers that are presented above focused on the strategic level and considered a static planning horizon, but there are also many papers that considered a dynamic planning horizon, like Melo et al. (2005), that proposed a dynamic mathematic framework, which includes dynamic planning, generic supply chain network structure,


external supply of materials, inventory opportunities, commodities distribution, facility configuration, availability of capital for investments and storage limitations. Similarly, Gebennini et al. (2007) considered a dynamic planning horizon and proposed innovative cost-based models and solutions for the location–allocation problem with safety stock level determination and customer service level optimisation. Routroy and Maddala (2009) and Routroy and Sanisetty (2007) discussed a generic model for multi-echelon supply chain inventory planning, considering the total SC cost, which consists of SC inventory capital, SC ordering/set-up cost and SC stockout cost for a maximum allowable SC inventory. In Manzini et al. (2008), the authors introduced the basis for the development of an innovative decision support systems platform, capable of integrating design, management, control and optimisation activities for a supply chain system. The authors expanded their theories in Manzini and Bindi (2009).

For RSC, like for the FSC, many literature reviews were analysed. Sasikumar and Kannan (2009) suggested a classification and in addition identified the different solution methodologies used in a RSC context and mapped the tools and techniques used with content classification. Melo et al. (2009) proposed a classification with respect to the network structure (recovery or closed-loop), the type of facilities that support reverse activities and the type of facilities for which location decisions are to be made. In Fleischmann et al. (1997), the authors defined a classification criterion of all papers, including reuse motivation, type of recovered items, form of reuse and involved actors, whereas in Fleischmann et al. (2000), the authors identified general characteristics of product recovery networks and compared them with traditional logistic structures. An example of model for reverse distribution logistical problems was developed in Jayaraman et al. (2003); the paper considered product recall, product recycling and reuse, product disposal and hazardous product return. An additional example was proposed in Gou et al. (2008), the purpose of the study was to find the optimal economic delivery batch size as well as the optimal handling batch size in order to minimise the open-loop RSC cost. While Lee et al. (2009) formulated a mathematical model aimed to minimise the total cost of reverse logistics shipping and fixed opening cost of the disassembly centres and processing centres.

Many papers considered simultaneously forward and reverse flows and analysed practical cases: Kroon and Vrijens (1995) considered the reuse of secondary packaging material, while Alshamrania et al. (2007) presented a study on reverse logistics motivated by blood distribution of the American Red Cross. Jayaraman et al. (2010) discussed a case study based on a product recovery problem faced by an electronics company and Kannan et al. (2010) proposed a genetic algorithm approach for solving a CLSC model for a case of battery recycling. Fuente et al. (2008) examined supply chain management as implemented in companies which deal simultaneously with forward and reverse logistics and considered the strategic and operational alignments, system interoperability, information share and coordination of activities. Akçalı et al. (2009) presented an annotated bibliography of models and solution approaches organised into two main sections that focus on RSC network design and CLSC network design. Fleischmann and Kuik (2003) considered a stochastic inventory model encompassing random item returns, where returns are independent of past demand and might be directly reused. Marin and Pelegrin (1998) proposed the so-called return plant location problem, in order to


minimise the total cost of plant opening, supply and return. Also, Lu and Bostel (2007) studied this problem and demonstrated that reverse flows influences the decisions about location and allocation. While Fleischmann et al. (2001) presented a generic facility location model for a CLSC and discussed the differences with traditional logistic settings, the authors proceeded analysing the impact of product return flows on logistic networks and showed that the influence of product recovery is very much context dependent. The model proposed in Fleischmann et al. (2001) was generalised in Salema et al. (2007), where a capacitated multi-product reverse logistic network model with uncertainty was developed. The uncertainty was also considered in the extended facility location MILP model proposed in Lieckens and Vandaele (2007).

In CLSC, like in FSC, some authors do not consider the location problem exclusively, e.g. Krikke et al. (2003) developed a quantitative modelling to support decision-making, concerning both the design structure of a product and the design structure of the logistic network, and others considered a dynamic planning horizon like Ko and Evans (2007), El-Sayed et al. (2008) and Salema et al. (2010), or an integration of strategic and tactical decisions, by considering two interconnected time scales: a macro and a micro time (Salema et al., 2009).

Table 1 summarises a classification of scientific literature dedicated to SC design, organised by aspects considered in the design models developed. This preliminary literature analysis shows that many approaches have been taken to design and optimise SCM, managing both inventory control and facility location, but is evident that recent research about SC has not yet focused on the CLSC, a critical issue that needs more investigation.

This paper takes into account the factors that are usually not considered in more traditional approaches:

a network structure with five level: plant, distribution centres (DC), distributor, customer and disposal facility

the installation, handling and inventory costs as well as transportation costs

the capacity constrains at the different facilities of the network

different transportation mode availability and economies of scale in transportation, thanks to a closed-loop shipment in forward–reverse flow

different type of products shipped.

The new and significant contribution of this paper is to make clear that it is possible to model separately direct and reverse flows with a significant reduction of the problem size as observed by other authors (Fleischmann et al., 2001), only in particular condition of input and with not strong constrains (e.g. warehouse capacity). In all other cases, it is necessary to adopt an integrated approach.


Table 1 Classification of the literature dedicated to SC design

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Table 1 Classification of the literature dedicated to SC design (continued)

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Table 1 Classification of the literature dedicated to SC design (continued)

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3 Cost function

The developed model addresses the CLSC design from a strategic point of view (long-term planning), considering a multi-echelon, multi-product and multi-production/distribution and multi-transportation system. For that reason, the model considers a static planning horizon, where the forward flows are considered average during the period.

Figure 1 presents a scheme illustrating the structure of this logistic network divided in five levels:

Plants

DCs

Distributors

Retailer

Disposal facilities in the reverse flows.

Each level can ship to all the other levels, and in the reverse flow, each facility can ship directly to the disposal site.

The network is based on a mixed-integer linear programming model that considers all the relevant cost factors and aims to optimise the SC network design. The presented model is flexible and able to model a CLSC with sequential and integral approach by just introducing new constrains in the reverse flow.

Figure 1 Example of CLSC


The minimisation of the total cost function, once the kind of reverse flows is defined (sequential or integral), and the input data, such as possible facility positions in the supply chain, the fixed installation cost for each facility, etc. are made clear, gives the following SC design outputs:

the plants, DCs and distributors open the direct flows respects, the quantity of primary product shipped from the plants to the customers through DCs and distributors the reverse flows of different kinds of products: defective returned products (i.e. warranty products) and disposal returned products (i.e. products shipped to the disposal facility) the kind of transportation mode to use.

Principal cost factors considered are the following: 1 Facilities installation costs: the cost of opening a new plant includes real estate

investment, including location and building, structures and security. The installation costs are defined about all kinds of facility (production plants, DCs and distributors). These costs are typically fixed costs and the saturation of facility capacity permits the economy of scale in the network management as expressed in the cost function of the proposed design model.

2 Production cost: this cost depends on the volume of products and includes cost of raw materials and components and cost of utilities (electricity and gas). An efficient and effective manufacturing process can reduce these costs, minimising the production lead time and reducing waste.

3 Handling cost: the handling cost includes cost of manpower and tools, necessary for the products to go through the facility. The proposed model considers only the variable costs that are a direct function of the volume moved and is dependent on the characteristics of the products.

4 Inventory cost: the inventory cost is created by goods inventory carrying costs (as tied up capital costs) and by warehousing and storage activities costs. The economic order quantity is a function of the total annual demand, the cost of a single product, the order emission cost and the opportunity cost, including insurance, taxes, storage space cost and inventory risk cost. In addition, any company needs to determine the appropriate safety stock, which needs to be adequate to fulfil the surplus of expected demand, and it is usually determined by the manager. Inventory costs are the sum of the cost of average stock and the cost of the safety stock.

5 Transportation cost: the transportation cost represents an important component of the total cost, so the decision of the modes of transportation (train, road, plane, rail and boat) is very important. The main factors that influence the selection are transportation cost, time, reliability and products safety. The model considers the variable transportation costs that depend on type, volume and weight of the products and also on the distances, transportation mode and supplier location respect to the retailer. The possibility to obtain economies of scale in transportation is defined in the model both for the forward and reverse transportation. In case of forward transportation, it is obtained thanks to a parameter in function of the position of the customers to serve, and in case of reverse transportation thanks to the combined forward–reverse shipment.


6 Reverse logistic cost: this cost includes costs of transportation, inventory and management of the reverse flow of products and packaging. Reverse logistic flow can be divided in process of restoration, re-engineering, recovering and reusing and waste disposal.

Figure 2 shows these principal cost factors considered in three different approaches: the classic forward SC design, the sequential CLSC design and the integral CLSC design.

In case of sequential approach, the forward flows are optimised in order to minimise the installation, production, handling, inventory and transportation costs to satisfy customer demand. While generally, the reverse flows are optimised focusing only on the backward flow of materials from customer to supplier (or alternate disposition) with the goal of maximising value from the returned item or minimising the total reverse logistics cost. The reverse flows in this approach do not present any routing constraints, which means that returns and disposal products can be shipped to all SC levels, independent of the forward flows.

In case of integral approach in our proposed model, the returned and disposal products have to follow the same route as the outgoing product, including transportation model, to allow transportation economies of scale.

Figure 2 Principal cost factors

4 The model

The linear programming model developed in this paper is formulated as follows:

4.1 Assumptions

The demand in each level of the SC has a standard distribution with average value Dand standard deviation D .


The retailer demand is derived by a forecasting process. While the distributors demand depends on the sum of the retailer demand satisfied, and the DC demand derived on the sum of distributors and retailer demand satisfied. A minimum service level has to be imposed at each level of the SC. There are not inventory and handling costs in the production plants because the finished products are directly shipped. The distance between each pair of SC actors are symmetrical in the forward and reverse flow. The quantity of products is indicated in cubic meters because the model considers facility saturation and carriers-to-volume saturation. In addition, distribution activities (handling, stocking, etc.) are influenced more by the kind of product volume than weight. Return products include the primary product itself returned after use, containers and defective items. The product disposal includes recyclable material, waste products and reusable components. In forward flows, the first level (plants) can ship to all the other levels, the second level (DCs) can ship to the third level, fourth level, etc. In the reverse flows, the first level (retailer) can ship to all the other levels, the second level (distributors) can ship to the third level, second level, etc. The cost of disposal activity is lower for the manufacturer than for the distributor because the manufacturer might be able to recover and reuse parts of the disposed product, lowering at the same time costs of production and disposal.

4.2 Indices I Plants 1 , ,i I

J DCs 1 , , j J

K Distributors 1 , , k K

L Retailer 1 , , l L

D Disposals 1 , , d D

P Products 1 , , p P

m Transportation mode 1 , , m M

f Fixed cost c Variable cost O Installation cost H Handling cost P Production cost T Transportation cost R Reverse cost D Disposal cost U Unsatisfied demand cost


4.3 Input data O

if , Ojf , O

kf Fixed installation cost of opening respectively a new plant i, a new DC j and a new distributor k

[€ year 1]

P,p ic Production cost per cubic meter of product p in plant I [€m 3]

H,p jc , H

,p kc Handling cost per cubic meter of product p respectively in DC j and in distributors k

[€m 3]

T,p mc Transportation cost per km and cubic meter of product p with

transportation mode m[€ km 1 m 3]

T *,p mc Transportation cost per km and cubic meter of product p with

transportation mode m in case of forward and reverse flows are simultaneously considered (CLSC network)

[€/ Km*m3]

R,p ic , R

,p jc , R,p kc Cost for cubic meter of defective returned product p

respectively in plant i, in DC j and in DC k[€/m 3]

D,p ic , D

,p jc , D,p kc Cost for disposal activities per cubic meter of product p

respectively in plant i, DC j and distributor k[€m 3]

U,p ic Unsatisfied cost per cubic meter of product p [€/m 3]

,i jd , ,i kd , ,i ld ,

,i dd

Distance between plant i and respectively DC j, distributor k,retailer l and disposal d

[Km]

,j kd , ,j ld ,

,j dd

Distance between DC j and respectively distributor k, retailer l and disposal d

[Km]

,k ld , ,k dd Distance between distributor k and respectively retailer l and disposal d

[Km]

,l dd Distance between retailer l and disposal d [Km]

jv Position factor for routing optimisation in the DC j. It represents the cost reduction due to DC’s position relative to the retailer

[%]

kv Position factor for routing optimisation in the distributors k. It represents the cost reduction due to the distributors’ position relative to the retailer

[%]

,p lD Total annual demand for product p from retailer l [m3/year]

,p jr , ,p kr , ,p lr Average time between two consecutive shipments of product p respectively in DC j, distributors k and retailer l

[year/shipments]

,S S p j , ,S S p k ,

,S S p l

Safety stock (SS) of product p respectively in DC j,distributors k and retailer l

[m3]

jh , kh Holding unit cost respectively in DC j and distributor k [1/year]

pp Unit value of product p [€m 3]

pR Percentage of defective returned products p respect the total shipment

[%]

pA Percentage of disposal products p with respect to the total shipment

[%]

pP Percentage of disposal products p with respect to the total items produced

[%]

,p iS Maximum production capacity p in plant i [m3/year] maxjI , max

kI Maximum storage capacity respectively of DC j and distributor k

[m3/year]


Considering, e.g. ,SSp j the SS is calculated as (Persona et al., 2007)

, , , ,S S L Tp j p j p j p jk (1)

where

,p jk : the number of standard deviations to be kept as safety stock for the product p in the DC j

,p j : standard deviation for the product p in the DC j

,LTp j : supplying lead time for product p in the DC j

4.4 Variable

iY 1 if plant i is open, 0 otherwise

jY 1 if DC j is open, 0 otherwise

kY 1 if distributor k is open, 0 otherwise

, , ,p m i lx , , , ,p m j lx ,

, , ,p m k lx

Percentage of demand of product p from retailer l satisfied respectively by plant i, DC j, distributor k and shipped with model transportation m

[%]

, , ,p m i jx , , , ,p m i kx Cubic meter of product p shipped from plant i respectively to DC j, distributor k with model transportation m

[m3/year]

, , ,p m j kx Cubic meter of product p shipped from DC j to distributork with model transportation m

[m3/year]

R, , ,p m i jy , R

, , ,p m i ky ,R

, , ,p m i ly

Quantity of returned defective products p to plant i respectively from DC j, distributor k and retailer l, shipped with model transportation m

[m3/year]

R, , ,p m j ky , R

, , ,p m j ly Quantity of returned defective products p to DC j respectively from distributor k and retailer l, shipped with model transportation m

[m3/year]

R, , ,p m k ly Quantity of returned defective products p from retailer l to

distributor k and shipped with the model transportation m[m

3/year]

D, , ,p m i jy , D

, , ,p m i ky ,D

, , ,p m i ly

Quantity of products to be disposed p respectively from DC j,distributor k and retailer l to plant i, shipped with model transportation m

[m3/year]

D, , ,p m j ky , D

, , ,p m l jy Quantity of products to be disposed p respectively from distributor k and retailer l to DC j, shipped with model transportation m

[m3/year]

D, , ,p m k ly Quantity of products to be disposed p from retailer l to

distributor k and shipped with model transportation m[m

3/year]

D, ,p i dy , D

, ,p j dy ,D

, ,p k dy

Quantity of products to be disposed p respectively from plant i,DC j, distributor k, to disposal d

[m3/year]

4.5 Model

The objective function of a multi-echelon, multi-product and multi-transportation mode CLSC model is given by the following equation:

Minimise TOT OC PC HC SC TC UC TRC TDC RC DC (2)


where TOT is the total cost [€/year]. The cost components in the objective function can be calculated using the following

relations:

Installation cost of opening new plant, DC and distributor [€/year]: O O OOC i i j j k k

i j k

Y f Y f Y f (3)

Production cost [€/year]: P P

, , , , , , , ,

P, , , , ,

PC p i p m i j p i p m i kp m i j p m i k

p i p m i l p lp m i l

c x c x

c x D (4)

Handling cost, given by a variable cost function of the quantity handled [€/year]:

H H, , , , , , , , , , ,HC p j p m i j p k p m i k p m j k

p m i j p m k i j

c x c x x (5)

Inventory cost, function of the safety stocks and of the average levels of the operative stocks inside the SC [€/year]:

, , , , ,

, , , , , , , ,

1SC SS2

1SS2

j p p j p j p m i jp m i j

k k p k p k p m i k p m j kp m k i j

h p r x

h p r x x

(6)

Transportation cost, given by a variable cost function of the quantity transported, distance travelled and transportation mode [€/year]:

T, , , , ,

T, , , , ,

,T, , , , ,

T, , , , ,

,T, , , , ,

,T, , , , ,

T C p m i j p m i jp m i j

p m i k p m i kp m i k

i lp m p m i l p l

ip m i l

p m j k p m j kp m j k

j lp m p m j l p l

jp m j l

k lp m p m k l p l

kp m k l

c d x

c d x

dc x D

v

c d x

dc x D

v

dc x D

v

(7)


Cost of non-satisfied demand [€/year]: U

, , , , , , , , , ,UC 1 p m i l p m j l p m k l p l pp m l i j k

x x x D c (8)

Cost of transporting reverse goods [€/year]: T * R

, , , , ,

T * R, , , , ,

,T * R, , , ,

T * R, , , , ,

,T * R, , , ,

,T * R, , ,

T R C p m i j p m i jp m i j


i lp m p m i l

p m i l i


j lp m p m j l

p m j l j

k lp m p k l

p m k l k

c d y

c d y

dc y

v

c d y

dc y

v

dc y

v

(9)

Cost of transporting disposal goods [€/year]: T * D

, , , , ,

T * D, , , , ,

,T * D, , , ,

T * D, , , , ,

T * D, , , , ,

T * D, , , , ,

,T *, , , ,

T D C p m i j p m i jp m i j


i lp m p m i l

ip m i l

p m i d p m i dp m i d


p m j d p m j dp m j d

j lp m p m j l

j

c d y

c d y

dc y

v

c d y

c d y

c d y

dc y

vD

,T * D, , , ,

T * D, , , ,

T * D, , , ,

p m j l

k lp m p m k l

kp m k l

p m k d p k dp m k d

p m l d p l dp m l d

dc y

v

c d y

c d y

(10)


Returned cost, given by a variable cost function of the quantity handling [€/year]:

R R R R, , , , , , , , , ,

R R R R, , , , , , , , , ,

R R R R, , , , , , , , , ,

RC p i p m i j p m i k p m i lp m i j k l

p j p m i j p m j k p m j lp j i k l

p k p m i k p m j k p m k lp k i j l

c y y y

c y y y

c y y y

(11)

Disposal cost, given by a variable cost function of the quantity handling [€/year]:

D D D D D, , , , , , , ,

D D D D, , , , , , ,

D C p i p i d p j p i j p j dp i d p j i d

p k p i k p j k p k dp k i j d

c y c y y

c y y y

(12)

4.6 Constraints

This constraint insures that the sum of flows exiting from each plant i to all the other member of the SC does not exceed the production capacity , ,p iS for each product p:

, , , , , , , , , , , ,p m i j p m i k p m i l p l i p im j m k m l

x x x D Y S p i (13)

This constraint insures that the sum of flows exiting from each DC j to each distributor kand retailer l is equal to the sum of the flow entering from all plant i:

, , , , , , , , , , ,p m j k p m j l p l p m i jm k m l m i

x x D x p j (14)

This constraint insures that the flows exiting from each distributor k to each retailer l are equal to the sum of the flow entering from all plant i and DC j:

, , , , , , , , , , ,p m k l p l p m i k p m j km l m i m j

x D x x p k (15)

This constraint insures that the sum of total flows entering each DC does not exceed the DC storage capacity:

R D, , , , , , , , , ,

R D R D, , , , , , , , , , , ,

D max, , ,

p j p m i j p m i j p m i jp m i

p m j k p m j k p m j l p m j lm k m i

p j d j jp

SS x y y

y y y y

y Y I j

(16)


This constraint insures that the sum of flows entering each distributor does not exceed the distributor storage capacity:

R D, , , , , , , , , ,

R D, , , , , , , , ,

R D D m ax, , , , , , , ,

S S

,

p k p m i k p m i k p m i kp m i

p m j k p m j k p m j km j

p m k l p m k l p k l k km l d

x y y

x y y

y y y Y I k

(17)

This constraint insures that the sum of the reverse flow entering to each plant does not exceed the plant storage capacity:

R D R D, , , , , , , , , , , ,

R D m ax, , , , , , ,

p m i j p m i j p m i k p m i kp m j k

p m i l p m i l i il

y y y y

y y Y I i

(18)

These constraints insure that each returned quantity corresponds to a percentage of shipping products. If we remove these constraints, the model changes from integral to sequential:

R, , , , , , , , ,p m i j p m i j py x R p m i j (19)

R, , , , , , , ,p m i k p i k py x R p m i k (20)

R, , , , , , , , , ,p m i l p m i l p l py x D R p m i l (21)

R, , , , , , , , ,p m j k p m j k py x R p m j k (22)

R, , , , , , , , , ,p m j l p m j l p l py x D R p m j l (23)

R, , , , , , , , , ,p m k l p m k l p l py x D R p m k l (24)

These constraints insure that each disposal quantity corresponds to a percentage of shipping products. If we remove these constraints, the model changes from integral to sequential:

D, , , , , , , , ,p m i j p m i j py x A p m i j (25)

D, , , , , , , ,p m i k p i k py x A p m i k (26)

D, , , , , , , , , ,p m i l p m i l p l py x D A p m i l (27)

D, , , , , , , , ,p m j k p m j k py x A p m j k (28)

D, , , , , , , , , ,p m j l p m j l p l py x D A p m j l (29)

D, , , , , , , , , ,p m k l p m k l p l py x D A p m k l (30)


This constraint insures that the sum of the disposal goods exiting from each retailer l to all the other members of the SC corresponds to a percentage of the total delivered products:

D D D D, , , , , , , , , , ,

, , , , , , , , , , ,

p m k l p m j l p m i l p l dm k m j m i d

p m k l p m j l p m i l p l pm k m j m i

y y y y

x x x D A p l (31)

This constraint insures that for the same distributor k, the sum of the exiting disposal goods is equal to a percentage of the arriving forward flows plus the disposal goods from the retailer.

D D D D, , , , , , , , , ,

, , , , , , ,

p m j k p m i k p k d p k lm j m i d l

p m j k p m i k pm j m i

y y y y

x x A p k (32)

This constraint insures that for the same DC j, the sum of the exiting disposal goods is equal to a percentage of the arriving forward flows plus the disposal goods from the retailer and the distributors.

D D D D, , , , , , , , , , ,

,

p m i j p j d p m j l p m j km i d m l m k

pij pm i

y y y y

x A p j (33)

This constraint insures that for the same plant i, the sum of the exiting disposal goods corresponds to a percentage of the product manufacturing plus the disposal goods entering from the retailer, distributors and DC:

D D, , , , , , , , , , ,

, , , , , , , , ,

D Dp i d p m i l p m i k p m i j

d m l m k m j

p i j p i k p i l p l pm j m k m l

y y y y

x x x D P p i (34)

This constraint insures that the safety stock ,S S p j of product p in DC j respects the first equation:

, , , ,S S L T , ,p j p j p j p jk p j (35)

This constraint insures that the safety stock ,S S p k of product p in distributors k respects the first equation:

, , , ,S S L T , ,p k p k p k p kk p k (36)


5 Applicative case

In this section, the mixed-integer linear programming CLSC model is applied to a case of logistics in the household appliance sector.

The analysed network consists of:

three manufacturers that produce household electrics are located in northern Italy (Vicenza, Siena and Novara) indicate respectively with (I1, I2, I3)

two central distributors, DC, (Modena, Foggia) indicate respectively with (J1, J2)

four regional distributors that covered a designated area (Bolzano, Piacenza, Pescara, Cosenza) indicate for with (K1, K2, K3, K4)

a total of 20 retailers clustered in 7 groups (see the map in Figure 3) indicate with (CL1, CL2, CL3, CL4, CL5, CL6, CL7).

two disposal facilities, one in northern (Brescia) and the second southern Italy (Salerno) indicate for with (DS1, DS2).

In this applicative case, we consider six different product families p (PF1:PF6) and for all these, we assume an average supplying lead time ( LTp ) of one week (1/52 year), equal for all the levels of SC (j, k). We impose a minimum service level in all the SC equal to 85% that corresponds to K = 1 for (35) and (36). We consider for a given value of the average demand D at each stage of SC a standard deviation D = 20% D.

The unsatisfied cost per cubic meter of product p is fixed as very high, so all demands are completely satisfied.

The disposal costs in plant are imposed to be approximately equal to a 1/3 of the unitary disposal costs in DC and in distributor for considering the possibility to recover part of the disposal product for next production activity and consequently reduce the quantity of new components to be purchased.

In this paper, we compare three different scenarios:

1 Scenario 1: considering only the forward flows.

2 Scenario 2: considering a supply chain in which forward and reverse flows are considered in sequence (each shipment is dedicated). In this scenario, the reverse transportation constrains are removed (formulas (19)–(30)).

3 Scenario 3: considering a supply chain in which forward and reverse flows are simultaneously considered. As a consequence, shipping is combined, i.e. the forward and the reverse flows have the same route, which creates economies of scale in the transportation costs. In this applicative case, in order to stress the closed-loop structure comparing with the classical SC structure, the transportation costs for the reverse flows in this scenario are 1/10 of the forward flows T * T

, ,( 1 / 10 ).p m p mc c

The input data are the same in all scenarios. The unit value of each product’s family Pp is expressed in Table 2, where are also indicated the percentages of defective returned product with respect to the total shipment, Rp, the percentage of disposal products with respect to the total shipment, Ap and the percentage of disposal products with respect to the total production, Pp. The distance matrix and the total demand matrix are reported in


Tables 3 and 4. The average time between two consecutive shipments is indicated in Table 5. The facilities installation costs and the maximum storage capacity of DC and distributors are defined in Table 6. The unitary cost for production, handling, reverse and disposal activity are indicated in Table 7. The specific transportation costs are expressed in Tables 8–11.

The model described above is implemented in GAMS software (www.gams.com), and the results are illustrated in Table 12.

1 the first column indicates the cost factors

2 the second column indicates the result considering only the forward flow (scenario 1)

3 the third column indicates the result considering forward the reverse flow in sequence (scenario 2)

4 the fourth column indicates the result of the integral closed-loop model (scenario 3).

Figure 3 Map of Italy

Table 2 Unit value of each product’s family

Product Description Product’s family average value [€ m 3] pR pA pP

PF1 Microwaves 400 0.05 0.35 0.05 PF2 Washing machines 250 0.06 0.36 0.02 PF3 Refrigerators 350 0.05 0.30 0.03 PF4 Air conditioners 500 0.06 0.31 0.02 PF5 Vacuum cleaner 220 0.06 0.30 0.02 PF6 Dishwasher 500 0.04 0.30 0.03


Table 3 Distance matrix [km]

J1 J2 K1 K2 K3 K4 CL1 CL2 CL3 CL4 CL5 CL6 CL7 DS1 DS2

I1 160 710 210 200 530 1,100 220 320 500 270 760 900 1,400 120 800 I2 200 590 450 300 400 730 520 550 550 160 380 720 1,080 350 480 I3 230 810 340 120 630 1,120 490 100 230 550 720 1,100 1,450 150 870 J1 250 150 406 910 500 300 400 350 530 750 1,250 160 650 J2 830 700 200 340 820 830 1,100 600 320 230 680 740 160 K1 450 130 600 630 800 1,050 1,500 210 890 K2 470 230 300 420 620 900 1,320 90 760 K3 720 700 800 400 230 400 950 560 340 K4 1,200 1,250 1,200 720 500 330 360 1,052 260 CL1 320 930 CL2 220 730 CL3 390 910 CL4 480 470 CL5 780 220 CL6 900 290 CL7 1,150 700

Table 4 Demand matrix [m3/year]

CL1 CL2 CL3 CL4 CL5 CL6 CL7

FP1 400 288 182 275 380 180 495 FP2 294 185 170 112 173 880 299 FP3 689 370 485 486 374 487 595 FP4 900 430 340 500 330 600 850 FP5 1,000 100 280 190 120 300 780 FP6 240 180 160 120 153 980 390

Table 5 Average time between two consecutive shipments [year]

DC Distributor Retailer

J1 J2 K1 K2 K3 K4 CL1 CL2 CL3 CL4 CL5 CL6 CL7

FP1 0.25 0.25 0.10 0.08 0.08 0.08 0.05 0.06 0.05 0.06 0.05 0.05 0.06 FP2 0.33 0.25 0.09 0.09 0.08 0.09 0.06 0.07 0.06 0.05 0.06 0.05 0.06 FP3 0.33 0.33 0.10 0.09 0.08 0.08 0.06 0.05 0.05 0.05 0.05 0.05 0.06 FP4 0.50 0.25 0.08 0.10 0.09 0.10 0.05 0.06 0.05 0.06 0.05 0.06 0.05 FP5 0.25 0.25 0.09 0.08 0.10 0.09 0.06 0.06 0.06 0.06 0.06 0.06 0.05 FP6 0.33 0.33 0.08 0.08 0.10 0.10 0.05 0.05 0.07 0.05 0.05 0.06 0.06


Table 6 Facilities installation costs and maximum storage capacity of DC and distributors

Plant DC Distributor

Iif [€/year]

maxiI

[m3/year]

Ijf

[€/year]

maxjI

[m3/year]

Ikf [€/year]

maxkI

[m3/year]

I1 260,000 260,000 J1 29,000 2,078,000 K1 23,000 1,230,000 I2 285,000 285,000 J2 23,000 2,078,000 K2 26,000 1,292,000 I3 290,000 290,000 K3 20,000 1,202,800 K4 28,000 1,200,800

Table 7 Unitary cost for production, handling, reverse and disposal activity

Plant DC Distributor

,Pp ic

[€ m3]

,Rp ic

[€ m3]

,Dp ic

[€ m3

]

,Hp jc

[€ m3]

,Rp jc

[€ m3]

,Dp jc

[€ m3]

,Hp kc

[€ m3]

,Rp kc

[€ m3]

,Dp kc

[€ m3]

I1 I2 I3 I1 I2 I3 I1 I2 I3 J1 J2 J1 J2 J1 J2 K1 K2 K3 K4 K1 K2 K3 K4 K1 K2 K3 K4

FP1 150 160 180 5.2 4.8 5.1 1.3 1.2 1.4 3.3 3.5 3.3 3.5 3.3 3.5 3.3 3.5 3.1 3.7 3.3 3.5 3.1 3.7 3 3.2 3.8 3.3

FP2 60 80 90 5.6 5.5 4.9 1.6 1.5 1.3 1.6 1.5 3.8 3.5 3.2 3.1 1.6 1.5 1.2 1.1 3.6 3.5 3.2 3.1 3.3 3.2 3 3.8

FP3 140 160 150 5.4 5.6 5.5 1.4 1.6 1.5 2.4 2.6 3 3.2 3.1 3.2 2.4 2.6 2.5 2.2 3.4 3.6 3.5 3.2 3.1 3.2 3.2 3

FP4 160 150 160 5.1 5.2 5 1.4 1.2 1 2.5 1.9 3.5 3.4 3.5 3.5 2.5 2.4 2.2 2.3 3.5 3.9 3.2 3.3 3.2 3.5 3 3.1

FP5 90 80 75 5.2 5.2 5.8 1.2 1.2 1.8 3 3.5 3.6 3.5 3.6 3.5 3.6 3.5 3.1 3 3.6 3.5 3.1 3 3.4 3.3 2.8 3.7

FP6 180 150 160 5.1 5.2 5 1.1 1.2 1 2.2 1.9 3.4 3.6 3.4 3.1 2.4 2.5 2.3 2.1 3.4 3.9 3.3 3.1 3.1 3.5 3 3

Table 8 Unitary cost for transportation in function of transportation mode from plant i[€ km 1 m 3]

J1 J2 K1 K2 K3 K4 CL1 CL2 CL3 CL4 CL5 CL6 CL7 D1 D2

Train.I1 0.08 0.08 0.34 0.353 0.343 0.354 8.85 8.83 8.81 100.84 8.83 8.81 8.84 0.1 0.1 Truck.I1 0.16 0.15 0.35 0.354 0.345 0.353 1.86 1.84 1.84 1.85 1.82 1.86 1.85 0.1 0.1 Train.I2 0.08 0.08 0.33 0.355 0.344 0.353 8.87 8.85 8.83 100.84 8.84 8.82 8.86 0.1 0.1 Truck.I2 0.14 0.15 0.35 0.352 0.356 0.357 1.84 1.82 1.86 1.85 1.83 1.81 1.86 0.1 0.1 Train.I3 0.08 0.08 0.35 0.358 0.344 0.353 8.85 8.83 8.85 100.83 8.83 8.85 8.83 0.1 0.1 Truck.I3 0.13 0.1 0.35 0.371 0.362 0.361 1.83 1.81 1.86 1.86 1.86 1.84 1.84 0.1 0.1

Table 9 Unitary cost for transportation in function of transportation mode from DC j[€ km 1m 3]

K1 K2 K3 K4 CL1 CL2 CL3 CL4 CL5 CL6 CL7 D1 D2

Train.J1 0.036 0.034 0.033 0.034 8.035 8.023 8.031 8.034 8.023 8.021 8.024 0.65 0.61 Truck.J1 0.031 0.035 0.034 0.033 0.36 0.34 0.34 0.35 0.32 0.26 0.35 0.66 0.64 Train.J2 0.032 0.033 0.032 0.032 8.037 8.025 8.033 8.034 8.034 8.032 8.026 0.67 0.63 Truck.J2 0.0333 0.034 0.035 0.032 0.34 0.32 0.36 0.35 0.33 0.21 0.36 0.64 0.66


Table 10 Unitary cost for transportation in function of transportation mode from distributors k[€ km 1m 3]

CL1 CL2 CL3 CL4 CL5 CL6 CL7 D1 D2

Train.K1 8.035 50.0013 8.0031 8.0034 100,000 8.0021 8.0024 0.65 0.61 Truck.K1 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.66 0.64 Train.K2 8.0037 8.0025 8.0033 8.0034 8.0034 8.0032 8.0026 0.67 0.63 Truck.K2 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.64 0.66 Train.K3 8.0037 8.0025 8.0033 8.0034 8.0034 8.0032 8.0026 0.65 0.65 Truck.K3 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.63 0.66 Train.K4 8.0037 8.0025 8.0033 8.0034 8.0034 8.0032 8.0026 0.67 0.65 Truck.K4 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.64 0.62

Table 11 Unitary cost for transportation from retailer l to disposal D [€ km 1m 3]

D1 D2

Train.CL1 8.085 8.081 Truck.CL1 0.96 0.94 Train.CL2 8.087 8.083 Truck.CL2 0.94 0.96 Train.CL3 8.085 8.085 Truck.CL3 0.93 0.96 Train.CL4 8.087 8.085 Truck.CL4 0.94 0.92 Train.CL5 8.087 8.83 Truck.CL5 0.94 0.96 Train.CL6 8.085 8.085 Truck.CL6 0.93 0.96 Train.CL7 8.087 8.085 Truck.CL7 0.94 0.92

Table 12 Disposal is 35% of the first product with relaxed capacity constraints: case 1 [€/year]

Forward (scenario 1)Forward + Reverse

(scenario 2) Forward Reverse

(scenario 3)

TOT 5,673,206 6,316,861 6,165,850

IC 386,000 386,000 393,000 PC 2,195,000 2,195,000 2,258,150 HC 73,633 67,253 61,426 SC 1,153,947 1,047,293 983,339 UC 0 0 0 TC 1,864,626 1,993,732 2,101,433 TRC 122,992 11,338


Table 12 Disposal is 35% of the first product with relaxed capacity constraints: case 1 [€/year] (continued)

Forward (scenario 1) Forward + Reverse


(scenario 3)

TOT 5,673,206 6,316,861 6,165,850

TDC 401,601 253,421 RC 34,838 13,456 DC 68,152 90,288 [Number] location of plants

[1] I1 (Vicenza) [1] I1 (Vicenza) [1] I3 (Novara)

[Number] location of DCs [1] J1 (Modena) [1] J1 (Modena) [1] J1 (Modena) [Number] location of distributors

[4] K1 (Bolzano) K2 (Piacenza) K3 (Pescara) K4 (Cosenza)


[3]

K2 (Piacenza) K3 (Pescara) K4 (Cosenza)

Flows

Tables 13–15 are organised in the same way. The results have be analysed in four different cases in function of the quantity of the

reverse flows and in function of the capacity constrains at DCs and distributors.

1 Case 1: the capacity constraints of plants, DCs and distributors are relaxed and the reverse flow given by the disposal products is 35% of the total products arrived to the retailer (also called first product) (Table 12).

2 Case 2: the capacity constraints of plants, DCs and distributors are relaxed and the amount of disposal products is 90% of the first product (Table 13).

3 Case 3: the capacity constraints of DCs and distributors are 50% of the retailer demand and the amount of disposal products is 35% of the first product (Table 14).

4 Case 4: the capacity constraints of DCs and distributors are 25% of the retailer demand and the amount of disposal products is 35% of the first product (Table 15).


Table 13 Disposal is 90% of the first product with relaxed capacity constraints [€/year]: case 2

Forward (scenario 1) Forward + Reverse


(scenario 3)

TOT 5,673,206 7,177,060 6,798,382

IC 386,000 360,000 393,000 PC 2,195,000 2,195,000 2,258,150 HC 73,633 61,033 61,426 SC 1,153,947 996,271 983,339 UC 0 0 0 TC 1,864,626 2,188,380 2,101,433 TRC 124,956 11,338 TDC 1,044,737 720,751 RC 32,816 13,456 DC 173,868 255,490 [Number] location of plants [1] I1 (Vicenza) [1] I1 (Vicenza) [1] I3 (Novara) [Number] location of DCs [1] J1 (Modena) [1] J1 (Modena) [1] J1 (Modena) [Number] location of distributors


[3] K1 (Bolzano) K3 (Pescara) K4 (Cosenza)

[3] K2 (Piacenza) K3 (Pescara) K4 (Cosenza)

Flows

Table 14 Disposal is 35% of the first product with distributor capacity at 50% of demand [€/year]: case 3

Forward (scenario 1)

Forward + Reverse (scenario 2)

Forward – Reverse (scenario 3)

TOT 5,883,316 6,894,742 6,325,135 IC 396,000 439,000 409,000 PC 2,258,150 2,258,150 2,195,000 HC 60,249 51,681 55,748 SC 919,342 818,029 887,570 UC 0 0 0 TC 2,249,576 2,511,940 2,407,377 TRC 205,769 12,916 TDC 538,594 260,841


Table 14 Disposal is 35% of the first product with distributor capacity at 50% of demand [€/year]: case 3 (continued)




RC 25,598 12,739 DC 45,981 83,945 [Number] location of plants

[1] I3 (Novara)

[1] I1 (Vicenza)

[1] I3 (Novara)

[Number] location of DCs

[1] J1 (Modena)

[2] J1 (Modena) J2 (Foggia)


[Number] location of distributors

[3] K1 (Bolzano) K2 (Piacenza) K4 (Cosenza)



Flows

I3J1

K1C

TT

C

CL1

CL5

CL6

CL7

CL3

CL4

CL2

C

C

C

C

C

C

C

C

K2

K4

J1

K1

T

CL1

CL5

CL6

CL7

CL3

CL4

CL2

DS1

CC

C

C

C

C

C

C

T

T

T

C

I1

T,CJ2

DS2K2

K3

K4

C

CL1

CL5

CL6

CL7

CL3

CL4

CL2TT

T

TC

C

C

C

C

C

C

T

T,C

C

C

I1J1

J2

DS1

DS2

K1

K2

K3

K4

Table 15 Disposal is 35% of the first product with distributor capacity at 25% of demand [€/year]: case 4




TOT 6,016,502 7,817,198 7,821,288 IC 409,000 724,000 724,000 PC 2,195,000 2,199,110 2,196,260 HC 58,719 37,088 32,242 SC 931,626 565,872 494,269 UC 0 0 0 TC 2,422,156 3,408,008 4,027,636 TRC 300,528 21,643 TDC 534,684 262,011 RC 16,181 9,234 DC 31,727 53,992 [Number] location of plants

[1] I1 (Vicenza)

[2] I2 (Siena)

I3 (Novara)

[2] I2 (Siena)

I3 (Novara) [Number] location ofDCs





Table 15 Disposal is 35% of the first product with distributor capacity at 25% of demand [€/year]: case 4 (continued)




[Number] location of distributors




Flows CL1

CL5

CL6

CL7

CL3

CL4

CL2

I1J1

K1T

TT

T

C

C

C

C

C

C

C

C

J2

T

T

CCC

C

K2

K3

K4

I3

J1

K1

T

CL1

CL5

CL6

CL7

CL3

CL4

CL2

DS1

C

C

C

C

C

C

C

J2

TT

T

T

TC

T,C

T,C

T

I2

DS2

K2

K3

K4

K2

K3

K4

CL1

CL5

CL6

CL7

CL3

CL4

CL2

DS1

TT

T

CC

C

C

C

C

C

C

T

T

T

K1

C

I3

I2

J1

J2 DS2

Case 1: this case describes a loop characterised by relaxed capacity constraints and a disposal equal to 35% of the initial product, where the network structure of ‘scenarios 1’ and ‘2’ are the same. This confirms Fleishmann’s conclusions that reverse flows can, in many cases, be implemented without major changes in existing forward production–distribution networks (Fleischmann et al., 2001). This study shows, on the other hand, that only in case of a sequential SC design approach, the Fleishmann’s conclusions are correct, while taking into consideration an integral SC design, the SC structure and flows change even in case of low reverse flows. In fact, ‘scenario 3’ of ‘case 1’ represents an optimal SC structure, where even if the production plant is different (more expensive), the reduction in transportation costs obtained reducing SC structure, makes this solution more desirable than the one illustrated in scenario 2. This highlights the importance of an integral approach in designing a SC in case of reverse flows.

Case 2: this case is an example of relaxed capacity constraints and a disposal equal to 90% of the first product. Differently from case 1 with these conditions, the SC structure between scenarios 1 and 2 are different. Moreover in scenario 2, some DC has direct shipments to retailers, without going through distributors, unlike scenario 1, which highlights the different SC structure in designing, considering the reverse flows also. In this case, like in ‘case 1’ the network structure of scenarios 2 and 3 are different and the solutions of the integral SC design approach are more desirable than the one illustrated in scenario 2. In addition, the SC structure of scenario 3 is the same as the ones of case 1, which demonstrates that not only the integral SC design approach provides cost-effective solutions, but also that it is a strong design and even incrementing the reverse flows to 90% of the first product, the network structure remains unaltered.

Case 3: this case considers capacity constrains of DCs and distributors equal to 50% of the retailer demand and disposal equal to 35% of the initial product. With these conditions, the comparison of the SC structure between scenarios 1 (forward flows only) and 2/3 (with reverse flows) is completely different in terms of opened facilities, even with low reverse flows quantity. In fact, capacity constrains in the SC’s intermediate levels (DCs, distributors) impose to open all the facilities, which inevitably brings


increasing costs. Otherwise, the total cost for scenario 3 is lower than the costs for scenario 2, highlighting again the importance of keeping an integral design approach.

Case 4: with capacity constrains of DCs and distributors very strong, equal to 25% of the retailer demand and disposal equal to 35% of the initial product, the comparison between scenario 1 SC structure (forward flows only) and scenario 2/3 structures (with reverse flows) is completely different in terms of opened facilities, even with low reverse flows quantity. Moreover, the high capacity constrains imposed in scenario 3 dictates a demand for direct shipments to retailer from the production plants. The closed-loop shipments give as consequence that the total cost of sequential or integral SC structural are almost the same.

Another element to consider in all four cases shown is relative to the disposal products (Tables 12–15).

If we assume that it is possible to recover part of the disposal products and to reduce waste, then the disposal cost is minimal at the production plants. In scenario 2, the disposal activities are made directly by costumers (100% of the disposal products are shipped directly from the retailer to the disposal facility), while in scenaio 3 the majority of disposal goods are transported to the prior levels of the SC, where parts are recovered and waste reduced (100% of the retailer disposal products are shipped from the retailer to the plant through a different supply chain level). This aspect is more and more frequent in different industrial contexts (automotive, household appliance sector, etc.) and is acquiring paramount importance not only for the economic savings it brings, but also for its environmental benefits.

5 Conclusions and future research

Considering the whole product life cycle (production, distribution, warranty, remanufacturing, recycle, disposal, etc.) and all the relative logistic flows (forward and reverse), the SC design methodology significantly changes respect to the classical approaches. The aim of this paper is double: on one hand, to present a new integrated methodology, based on mixed-integer programming for the integral closed-loop network design, and on the other hand, to evaluate the different SC design approaches in case of forward flows only, and in case of forward and reverse flows. This paper considers a multi-echelon, multi-product, multi-production/distribution system with multi-transportation and tests the model in real application cases. Following are the most relevant findings of our study:

The structure of a forward SC can be implemented for reverse flows without requiring major changes in existing production–distribution networks, only if the quantity of reverse flows is limited and the capacity constrains at the intermediate levels of the SC (DCs, distributors) are relaxed. If such conditions are not satisfied, the introduction of a reverse flow drastically alters the SC structure.

Many studies do not consider the capacity constrains, but with the introduction of constrains, as in the proposed model, the SC structure significantly changes.


As demonstrated by the applicative case, the proposed integral model in designing and configuring multi-stage and close-loop SC consistently maintains the same optimal SC structure, even when the principal inputs are changing. In fact, looking at cases 1 and 2, where the amount of disposal goods in the reverse flows changes considerably, the optimal SC structure given by the proposed model remains the same.

An integral approach in designing SC, where shipping is combined and forward and reverse flows have the same route, incurs in costs that are always lower or equal to those of a sequential design, in which each forward and reverse shipment is dedicated and singularly optimised.

Many models do not considered disposal costs, but the proposed integral design approach in SC shows that if the production plant has the capabilities to recover and to reprocess part of the disposal product, then it is possible to reduce the total costs in SC, recycling components products, with a reduction of waste and disposal costs.

In addition, the model permits to identify the best transportation mode in function of the volume of shipped products and the distance and evidence than considerable economy of scale are possible in the reverse flows, considering closed-loop routes in the transportation.

More research about reverse activities in logistics, especially in CLSCs, will definitely be developed, given the great importance today’s market is putting on environmental awareness.

Three aspects can be mentioned to justify reverse activities in SC (Wang et al., 2007): economic aspects (the possibility of recapturing value of used products), government directives (e.g. European Union WEEE Directive) and consumer pressure (e.g. return of defective products). In all these three aspects, both environmental and logistical aspects are considered. In fact, every product generated, transported, used and discarded within the supply chain causes a certain impact on the environment (Tsoulfas and Pappis, 2006).

First of all, it is important to give companies methodologies that can be easily followed in function of few critical parameters depending on their business (i.e. number and location of retailer, retailer demand, type of product, raw material costs, transportation costs, disposal costs, etc.), to define if it is economically convenient to develop a CLSC. For example, reprocessing disposal products instead of leaving retailer to dispose them could become a valuable option. On the other hand, it is important to make companies environmentally conscious of the impact of the product life cycle for the environment and inside the SC network.

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Multi-stage supply network design in case of reverse flows: a closed-loop approach

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